Exponential sums and differential equations:
This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of e...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[1990]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 124 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400882434 |
| DOI: | 10.1515/9781400882434 |
Internformat
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| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) | ||
| 520 | |a This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case | ||
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Datensatz im Suchindex
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| author | Katz, Nicholas M. 1943- |
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| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400882434 |
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| id | DE-604.BV043712503 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:08Z |
| institution | BVB |
| isbn | 9781400882434 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029124731 |
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| psigel | ZDB-23-DGG ZDB-23-PST |
| publishDate | 1990 |
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| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Katz, Nicholas M. 1943- (DE-588)141265558 aut Exponential sums and differential equations Nicholas M. Katz Princeton, NJ Princeton University Press [1990] © 1990 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 124 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case In English Differential equations Exponential sums Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Exponentialsumme (DE-588)4201355-0 gnd rswk-swf Lineare Differentialgleichung (DE-588)4206889-7 gnd rswk-swf Exponentialsumme (DE-588)4201355-0 s Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 Lineare Differentialgleichung (DE-588)4206889-7 s 2\p DE-604 Erscheint auch als Druck-Ausgabe 0-691-08598-6 Annals of Mathematics Studies number 124 (DE-604)BV040389493 124 https://doi.org/10.1515/9781400882434?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Katz, Nicholas M. 1943- Exponential sums and differential equations Annals of Mathematics Studies Differential equations Exponential sums Differentialgleichung (DE-588)4012249-9 gnd Exponentialsumme (DE-588)4201355-0 gnd Lineare Differentialgleichung (DE-588)4206889-7 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4201355-0 (DE-588)4206889-7 |
| title | Exponential sums and differential equations |
| title_auth | Exponential sums and differential equations |
| title_exact_search | Exponential sums and differential equations |
| title_full | Exponential sums and differential equations Nicholas M. Katz |
| title_fullStr | Exponential sums and differential equations Nicholas M. Katz |
| title_full_unstemmed | Exponential sums and differential equations Nicholas M. Katz |
| title_short | Exponential sums and differential equations |
| title_sort | exponential sums and differential equations |
| topic | Differential equations Exponential sums Differentialgleichung (DE-588)4012249-9 gnd Exponentialsumme (DE-588)4201355-0 gnd Lineare Differentialgleichung (DE-588)4206889-7 gnd |
| topic_facet | Differential equations Exponential sums Differentialgleichung Exponentialsumme Lineare Differentialgleichung |
| url | https://doi.org/10.1515/9781400882434?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
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